"Bloody thou art, bloody will be thy end; Shame serves thy life and doth thy death attend." So the Duchess of York curses Richard III in Shakespeare's eponymous play, predicting the king's demise at the battle of Bosworth. More than half a millennium after Bosworth, Yorkists and their enemies are still fighting over his corpse. The Plantagenet Alliance – which describes itself as "collateral" or non-direct descendants of Richard and thereby grants itself licence to speak on his behalf – has launched a daring high court assault on the University of Leicester over the location of Richard's reburial site. The Plantagenets have asked for the matter to be put out for consultation with the public, the Queen, English Heritage and themselves, buying time to further the case for reinterment in York. The university, meanwhile, insists on Leicester, the city where he was found next to a painted letter "R" in a council car park.

Much is at stake. A substantial tourist boom is expected to come to the city that can call itself Richard III's resting place. Leicester's new £4m Richard visitor centre is expected to attract 100,000 visitors a year. York, already blessed by cultural heritage with its Roman and Viking past and its gothic minster, would doubtless benefit, too.

But the arguments extend beyond the purely economic. The Plantagenet Alliance's case is built on the assertion that the discovery of the body of a former English monarch is unprecedented and a matter of national importance, with which few would disagree, and that public consultation is therefore essential. Its argument that it should have a say, in the same way that descendants of a soldier killed at the Somme would be consulted by the War Graves Commission, does not, however, stand up to scrutiny. The Plantagenets' family connections to the king are far more tenuous: Richard had no surviving children but five siblings, and now could have several million similarly distant descendants. The alliance's court battle also smacks of opportunism: it did not exist at the time of the extraordinary press conference in February last year when Richard's identity was announced. Most persuasive for Leicester, however, may be the argument that the decision has already been made by an English monarch: in 1485, Richard's successor, Henry VII, would have likely overseen the disposal of the royal corpse and approved the burial site at Greyfriars Friary.

The Plantagenet Alliance is asking the judges to overrule the terms of the dig licence, which stipulated reburial at Leicester cathedral. The more discussion of the extraordinary "king in the car park" find, the better. But his bones belong in Leicester.